Principles of Modern Radar - Volume 2 1891121537

136 CHAPTER 4 MIMO Radar4.5.2 MIMO Range ResponseIn the previous section, we described the angular point spread function of a MIMO radar,which described the sidelobes of the effective antenna pattern. Similar sidelobe structureswill exist in the range domain, just as they do in traditional radar systems.We extend the definition of the MIMO signal correlation matrix of (4.11) toR φ (τ) =∫ ∞−∞ (t) (t − τ) H dt (4.33)Note that our analysis of the spatial characteristics of a MIMO radar focused on thecase where τ = 0, the range bin of interest. This dependence on lag, τ, will allow us tocharacterize the influence a target at a particular range will have in bins up- and down-range.The range response of a set of MIMO waveforms with correlation matrix R φ (τ) isgiven byh (t,θ; θ 0 ) =a (θ 0) H R ∗ φ (t) a (θ)√a (θ 0 ) H R ∗ φ (0) a (θ 0 )(4.34)This result is extended to consider a Doppler offset in addition to a range offset in [15].4.5.3 Example: Up- and Down-ChirpSince many radar systems use linear frequency modulated (LFM) waveforms, also calledan LFM chirp, a natural method for generating two approximately orthogonal waveformsis to use one chirp with increasing frequency and another with decreasing frequency.Time-frequency representations describing a notional pair of such signals is shown inFigure 4-8. Note that these signals possess the same frequency support.FIGURE 4-8Time-frequencyrepresentation ofthe up- anddown-chirps. Ineach case, thebandwidth is50 MHz and thepulse width is 5 μs.Frequency (MHz)50403020100−10Up Chirp45403530Frequency (MHz)50403020100−10Down Chirp45403530−20−20−3025−3025−40−501 2 3 4Time (µs)20−40−501 2 3 4Time (µs)20